The

solar incidence angle ? (in degrees) is a function of the angle of solar

declination ? (in degrees), the latitude of the location of the photobioreactor

? (in degrees), the inclination of the photobioreactor with respect to the

ground ? (in degrees), the azimuthal angle ? (in degrees) as well as the solar

hour angle ? (in degrees) 18. The solar

incidence angle is given by the following equation

For

two sides of the photobioreactor, the angle of incidence is calculated based on

the solar azimuthal and inclination angle for the front and back sides of the

reactor. The azimuthal angle and the angle of inclination of the reactor, for

the front and back side, are computed using the following equations:

The

angle of solar declination ? is computed by the following

equation:

where,

N is the number of the day in the year.

The solar

hour angle ?, is given by the following equation:

where,

is

a function of the actual time t (h), longitude of the location of the reactor ?

(in degrees), meridian of the location of the reactor ? (in degrees) and the

equation of time e. The solar time (

is

computed by the following equations:

The

solar zenith angle

(in degrees) and the angle of elevation of the

Sun

(in degrees) are complementary to each other

and the calculated by the following equations:

The

azimuthal angle ? (in degrees) is given by the following

equation:

In

order to model the solar irradiance on flat panel photobioreactor the direct

and diffuse solar irradiance are taken into account. As solar irradiance data

are measured perpendicular to the surface of the earth, geometric factors are

introduced to obtain solar irradiance on the front and back sides of the

photobioreactor based on its inclination with respect to the surface of the

earth. The front side and back side geometric factors for the reactor for

direct solar irradiance are computed by the following set of equations:

The

geometric factors for the diffuse solar irradiance are a function of the angle

of inclination of the reactor with respect to the ground, ? (in degrees). The

geometric factors for the front side and back side of the reactor for diffuse

solar irradiance are computed by the following equations:

The

geometric factors for the ground reflected diffuse solar irradiance for the

photobioreactor is a function of the reflectivity of the ground surface ?.

Following the same approach as above the geometric factors are computed by the

following equations:

The

total solar irradiance on the front and back side of the photobioreactor (

) (W/m2) is computed by the

following equations:

Light distribution in parallel flatpanel

photobioreactors

In

large scale microalgae cultivation in photobioreactors often a series of

reactors are placed parallel to each other. Such a configuration results in

shading and significant part of the reactor surface is unable to receive direct

solar irradiance. The height of shadow on vertical photobioreactor panels is

given by the following equation:

where,

h (m) is the height of the reactor,

(m) is the distance between the parallel

reactor panels and

is

the solar zenith angle (in degrees). In order to perform the simulation the

panel is divided into two parts. The upper part of the panel receives both the

direct and diffuse solar irradiance whereas the lower part receives only

diffuse solar irradiance. The separation between these two parts depends on the

solar zenith angle and it is computed for every time step during the day time. Parallel

positions of the photobioreactors also influence the penetration of diffuse

solar irradiance in the space between the panels, where the intensity decreases

from the top to the bottom. Thus, the geometric factors of diffuse solar

irradiance for the front and back side of the reactor panels become a function

of height and are given by the following equations: